How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics
Many people here know that I am a “Bohmian”, i.e. an adherent of a very non-orthodox interpretation of quantum mechanics (QM). Indeed, in the past, I have published a lot of papers on Bohmian mechanics in peer-reviewed journals from 2004 to 2012. So how can I not worry and love orthodox QM? As a “Bohmian”, shouldn’t I be strictly against orthodox QM?
No. If by orthodox QM, one means instrumental QM (which is well explained in the book “Quantum Theory: Concepts and Methods” by A. Peres), then orthodox QM is fully compatible with Bohmian QM. I am not saying that they are equivalent; indeed Bohmian QM offers answers to some questions on which instrumental QM has nothing to say. But I am saying that they are compatible, in the sense that no claim of instrumental QM contradicts any claim of Bohmian QM.
But still, if instrumental QM has nothing to say about certain questions, then why am I not worried? As a “Bohmian”, I certainly do not consider those questions irrelevant. So how can I not worry about it when it says nothing about questions that I find relevant?
The answer is that I stopped worrying and learned to love orthodox QM precisely because I know about Bohmian QM. But let me explain it from the beginning.
I always wanted to study the most fundamental aspects of physics. Consequently, as a student of physics, I was much more fascinated by topics such as particle physics and general relativity than by topics such as condensed matter physics. Therefore, my graduate study in physics and my Ph.D. were in high-energy physics. Nevertheless, all the knowledge about quantum field theory (QFT) that I acquired as a high-energy physicist did not help me much to resolve one deep puzzle that bothered me about QM. The thing that bothered me was how could Nature work like that. How could that possibly be? What could be a possible physical mechanism behind the abstract rules of QM? Should one conclude that there is no mechanism at all and that standard QM (including QFT) is the end of the story?
But then I learned about Bohmian QM, and that was a true revelation. It finally told me a possible story of how could that be. It didn’t tell how it is (there is no direct evidence that Bohmian mechanics is how Nature works), but it did tell how it might be. It is comforting to know that behind the abstract and seemingly paradoxical formalism of QM may lie a simple intuitive mechanism as provided by Bohmian QM. Even if this mechanism is not exactly how Nature works, the simple fact that such a mechanism is possible is sufficient to stop worrying and start to love instrumental QM as a useful tool that somehow emerges from a more fundamental mechanism, even if all the details of this mechanism are not (yet) known.
However, something important was still missing. Bohmian QM looks nice and simple for non-relativistic QM, but how about relativistic QFT? In principle, Bohmian ideas of that time worked also for relativistic QFT, but they did not look so nice and simple. My question was, can Bohmian ideas be modified such that it looks nice, simple, and natural even for relativistic QFT? That question motivated my professional research on Bohmian QM and I published a lot of papers on that.
Nevertheless, I was not completely satisfied with my results. Even though I made several interesting modifications to Bohmian QM to incorporate relativistic QFT, neither of those modifications looked sufficiently simple and natural. Moreover, in arXiv:1309.0400, the last specialized paper on Bohmian mechanics I wrote, a referee found a deep conceptual error that I was not able to fix. After that, I was no longer trying to modify Bohmian QM in that way.
Nevertheless, partial satisfaction came from a slightly different angle. In an attempt to make sense of the local non-reality interpretation of QM, I developed a theory of solipsistic hidden variables which is a sort of a hybrid between Bohmian and Copenhagen QM. In this theory, an observer does play an important role, in the sense that Bohmian-like trajectories exist only for degrees of freedom of the observer and not for the observed objects. That theory helped me to learn that, to understand why we observe what we observe, it is not necessary to know what exactly happens with observed objects. Instead, as solipsistic hidden variables demonstrate, in principle it can be understood even if the observed objects don’t exist! It was a big conceptual revelation for me that shaped my further thinking about the subject.
But it does not mean that I became a solipsist. I don’t believe that observed objects don’t exist. The important message is not that observed objects might not exist. The important message is that the exact nature of their existence is not so important to explain their observation. That idea helped me a lot to stop worrying and learn to love orthodox QM.
But that was not the end. As I said, in my younger days, my way of thinking was largely shaped by high-energy physics and not by condensed matter physics. I thought that condensed-matter physics cannot teach me much about the most fundamental problems in physics. But it started to change in 2010, when, by accident, I saw in Feynman’s Lectures on Physics that Bohmian mechanics is related to superconductivity (see here) That suddenly made me interested in superconductivity. But superconductivity cannot be understood without understanding other more basic aspects of condensed-matter physics, so gradually I became interested in condensed-matter physics as a field. One very interesting thing about condensed-matter physics is that it uses QFT formalism which is almost identical to QFT formalism in high-energy physics, but the underlying philosophy of QFT is very different. Condensed-matter physics taught me to think about QFT in a different way than I was used to as a high-energy physicist.
One of the main conceptual differences between the two schools of thought on QFT is the interpretation of particle-like excitations resulting from canonical quantization of fields. In high-energy physics, such excitations are typically interpreted as elementary particles. In condensed-matter physics, they are usually interpreted as quasiparticles, such as phonons. Since I was also a Bohmian, that led me to a natural question: Does it make sense to introduce a Bohmian trajectory of a phonon? An obvious (but somewhat superficial) answer is that it doesn’t make sense because only true particles, and not quasiparticles, are supposed to have Bohmian trajectories. But what is a “true” particle? What exactly does it mean that a photon is a “true” particle and a phonon isn’t?
It was this last question that led me to my last fundamental insight about Bohmian mechanics. As I explained in Sec. 4.3 of arXiv:1703.08341 (accepted for publication in Int. J. Quantum Inf.), the analogy with condensed-matter quasiparticles such as phonons suggests a very natural resolution of the problem of Bohmian interpretation of relativistic QFT. According to this resolution, the so-called “elementary” particles such as photons and electrons described by relativistic QFT are not elementary at all. Instead, they are merely quasiparticles, just as phonons. Consequently, those relativistic particles do not have Bohmian trajectories at all. What does have Bohmian trajectories are some more fundamental particles described by non-relativistic QM. Non-relativistic QM (together with Bohmian interpretation) is fundamental, while relativistic QFT is emergent. In this way, the problem of the Bohmian interpretation of relativistic QFT is circumvented in a very elegant way.
There is only one “little” problem with that idea. There is no experimental evidence that such more fundamental non-relativistic particles exist in Nature. Perhaps they will be discovered one day in the future, but at the moment it is only a theory. It is not even a proper theory, because it cannot tell anything more specific about the exact nature of those hypothetical non-relativistic particles.
Nevertheless, there are at least two good things about that. First, unlike most other versions of Bohmian mechanics, this version makes a testable prediction. It predicts that, at very small distances not yet accessible to experimental technology, Nature is made of non-relativistic particles. Second, at distances visible by current experimental technology, this version of Bohmian QM says that Bohmian trajectories are irrelevant. This means that, as far as relativistic QFT is concerned, I do not need to worry about Bohmian trajectories and can love orthodox QFT, without rejecting “common sense” in the form of non-relativistic Bohmian mechanics on some more fundamental scale. That’s how I finally stopped worrying and learned to love orthodox QM.
Theoretical physicist from Croatia
My problem with your signature is that it seems that there is quite a bit of wishful thinking motivated only by the desire that BM is the true description of the world."The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them. In this methodological uncertainty, one might suppose that there were any number of possible systems of theoretical physics all equally well justified; and this opinion is no doubt correct, theoretically. But the development of physics has shown that at any given moment, out of all conceivable constructions, a single one has always proved itself decidedly superior to all the rest."
– Einstein
You may call it wishful thinking, I call it physical hypothesis motivated by physical intuition based on BM. In a sense, any scientific hypothesis can be thought of as wishful thinking, but it doesn't make the hypothesis less scientific. The 19th century hypothesis that matter is made of atoms was also an example of "wishful thinking".
“The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.”
― George Bernard Shaw"Long may Louis de Broglie continue to inspire those who suspect that what is proved by impossibility proofs is lack of imagination."
– John Stewart Bell
Not sure if Shaw meant physics, I suspect that by the world he probably meant society.
The way your proposal looks to me, in line of your example, is as someone proposing that atoms don't exist and it only appears that way. And he suggests that based on his favorite model."One should not reproach the theorist who undertakes such a task by calling him a fantast; instead, one must allow him his fantasizing, since for him there is no other way to his goal whatsoever. Indeed, it is no planless fantasizing, but rather a search for the logically simplest possibilities and their consequences."
– Einstein
I think it cannot explain why the unique measuremenet outcomes appear. For instance, in the two-slit experiment with a single photon, why do we detect photon at a single position only?The mathematical reason for unique measurement outcomes in single particle wavefunctions is due to the non-local nature of the system i.e. the presence of some cohomology element ##eta##: for any sufficiently small open subregion ##G'## of a region ##G##, the cohomology element ##eta## vanishes when restricted down to ##G'##. See this thread for elaboration and/or further discussion.
In either case, the hydrodynamic formulation doesn't specifically set out to answer such a question in the first place, even though it might be able to if one would select the correct nonlinear PDE to generalize towards which naturally contains such non-local properties.
Excuse me, I should have clarified earlier; I meant what is your opinion on the mathematical physics (as explained here) of the hydrodynamic formulation of QM? Do you view such mathematical work as pure baseless numerology? I get the feeling many theoretical physicists do.
For more background, here is a recent survey article by fluid dynamicist John Bush (MIT, Applied Math), primarily described in section 4 and 5 (feel free to skip section 1-3, if you are already familiar with it and/or like me not necessarily so much interested in experimental analogues): Pilot Wave Hydrodynamics.
Not sure if Shaw meant physics, I suspect that by the world he probably meant society.
You may call it wishful thinking, I call it physical hypothesis motivated by physical intuition based on BM. In a sense, any scientific hypothesis can be thought of as wishful thinking, but it doesn't make the hypothesis less scientific. The 19th century hypothesis that matter is made of atoms was also an example of "wishful thinking".The way your proposal looks to me, in line of your example, is as someone proposing that atoms don't exist and it only appears that way. And he suggests that based on his favorite model.
My problem with your signature is that it seems that there is quite a bit of wishful thinking motivated only by the desire that BM is the true description of the world.You may call it wishful thinking, I call it physical hypothesis motivated by physical intuition based on BM. In a sense, any scientific hypothesis can be thought of as wishful thinking, but it doesn't make the hypothesis less scientific. The 19th century hypothesis that matter is made of atoms was also an example of "wishful thinking".
“The reasonable man adapts himself to the world: the unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man.”
― George Bernard Shaw
My recent paper "Bohmian mechanics for instrumentalists" linked in my signature below is a sort of an elaborated version of the insight at the beginning of this thread.My problem with your signature is that it seems that there is quite a bit of wishful thinking motivated only by the desire that BM is the true description of the world.
In which sense is BM a "computational tool"? It only adds the trajectories a posteriori when the wave function is calculated from "conventional QT".There is a way to compute trajectories first and then to infer the wave function from it. See e.g. https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.82.5190
I am not an expert for applications of BM as a computational tool, but I think the Wyatt's book is the best.In which sense is BM a "computational tool"? It only adds the trajectories a posteriori when the wave function is calculated from "conventional QT". I always considered BM as just an alternative deterministic non-local interpretation of non-relativistic QT but not that one can establish some practical calculational tools using it.
What is your opinion of the hydrodynamic formulation?I think it cannot explain why the unique measuremenet outcomes appear. For instance, in the two-slit experiment with a single photon, why do we detect photon at a single position only?
I am not an expert for applications of BM as a computational tool, but I think the Wyatt's book is the best.Agreed here. Even from a purely mathematical PDE point of view, the striking similarity between QM and hydrodynamics, i.e. the so-called quantum hydrodynamics, absolutely fascinates me. A mathematical physicist by the name of R. Carroll rejoins in this fascination, quoted here.
What is your opinion of the hydrodynamic formulation?
I only read it today too, and as someone who is also fascinated by the Bohmian interpretation (but only acquinted with it at a superficial level), I enjoyed it thoroughly. Many thanks.
Demystifier submitted a new PF Insights post@Demystifier, I did not read your article until today, thank you for a very interesting account! And an extra thumbs up from me for the very funny title! :biggrin:
My recent paper "Bohmian mechanics for instrumentalists" linked in my signature below is a sort of an elaborated version of the insight at the beginning of this thread.
It seems, but we don't know if this persists at even smaller distances than available by current experimental technology. The default hypothesis is that it persists, but a hypothesis that it doesn't is also legitimate and Bohmian mechanics is not the only motivation for such a "heretic" hypothesis. See e.g. Horava gravity.As before, i have a different angle but i agree to this 100%
My default hypothesis is that lorentz invarance (and spacetime itself for that matter) are indeed emergent at lower(but still high) energies. I think that at very high energies causality become more stochastic and the arrow of time get more and more uncertain and thus lorentz symmetry loose its meaning.
Thus any no-go claims as to what isnt possible based on extrapolating lorentz invariance to infinity might in fact misguide us.
/Fredrik
And the Hidden-measurements interpretation seems saying "Cat knows, ask him…"Asking cat does not help much: https://arxiv.org/abs/1406.3221
And the Hidden-measurements interpretation seems saying "Cat knows, ask him…"
I might have more comments later but i seem to never get enough time…until then:
I just wanted to applaud Demystifier not letting what is not conceptually satisfactory pass!
The thing that bothered me was how could Nature work like that? How could that possibly be? What could be a possible physical mechanism behind the abstract rules of QM? Should one conclude that there is no mechanism at all and that standard QM (including QFT) is the end of story?I feel exactly the same way, even though my hypothesis may lie in a different direction. Power to you for not swallowing what is really substandard reasoning, and not loosing focus! That in an environment where it is a fact that "most people" seem to ignore these things probably for pragmatic reasons. I have found this extremely disturbing.
Thanks for sharing your journey!
/Fredrik
My question is about Copenhagen. Is Sabine right that it is about "I don't care if the cat is dead"?This is only one of version of Copenhagen. For other versions see https://arxiv.org/abs/1703.08341 Sec. 2.1.
if I have to buy just one book.. which of the following is good:
https://www.amazon.com/Trajectory-Description-Quantum-Processes-Applications/dp/3642179738
https://www.amazon.in/Trajectory-Description-Quantum-Processes-Fundamentals/dp/3642180914/257-7565493-7958461?_encoding=UTF8&*Version*=1&*entries*=0&portal-device-attributes=desktop
https://www.amazon.com/Quantum-Dynamics-Trajectories-Hydrodynamics-Interdisciplinary/dp/0387229647I am not an expert for applications of BM as a computational tool, but I think the Wyatt's book is the best.
I just found this site:
Problems with Bohmian mechanics <mod: approved link>
While this web site is (like any web site) not peer reviewed, it contains numerous references to peer-reviewed work substantiating that the claims made there are not those of a crank but have a significant support in the scientific community. In fact, much of the contents of the site may be viewed as a review of critiques of Bohmian mechanics. Some references to web sites supporting Bohmian mechanics are also given.
Enjoy!BM is good to differentiate between the wave function and the object.. the so called trajectories.. if I have to buy just one book.. which of the following is good:
https://www.amazon.com/Trajectory-Description-Quantum-Processes-Applications/dp/3642179738
https://www.amazon.in/Trajectory-De…&*entries*=0&portal-device-attributes=desktop
https://www.amazon.com/Quantum-Dynamics-Trajectories-Hydrodynamics-Interdisciplinary/dp/0387229647
BM can be saved if the original idea of this thread which is about quasiparticles and fundamental particles in condense matter analogy is correct (which Neumaier shared site doesn't mention).
But if BM is just wrong and can be proven to be wrong. Then we either have MWI and Copenhagen as the remaining viable candidates. I prefer Copenhagen.
Sabine is writing a book about the whole thing. She removed the following illustration because she explained her book not funny:
View attachment 212256
Sabine explains in: http://backreaction.blogspot.com/ (September 6, 2017 entry)
"Why did I remove it? To begin with it was pretty pointless. Also, style doesn't fit with the rest of the book. It's not a funny book really. Then I removed the whole explanation in the text about consistent histories because I found it to be unnecessary and more confusing than enlightening, and somehow I felt with only 5 items the list wouldn't really be a list.
I think in the end I just got fed up with it and that was that."
Bhobba favorite is consistent histories.. so other physicists don't like it.
My question is about Copenhagen. Is Sabine right that it is about "I don't care if the cat is dead"?
It seems our discussions are more advanced that I wonder if the new books coming out would be more complete or breathtaking that shared in PF.
I just found this site:
Problems with Bohmian mechanics <mod: approved link>
While this web site is (like any web site) not peer reviewed, it contains numerous references to peer-reviewed work substantiating that the claims made there are not just those of a crank but have a significant support in the scientific community. In fact, much of the contents of the site may be viewed as a review of critiques of Bohmian mechanics. Some references to web sites supporting Bohmian mechanics are also given.
Enjoy!
My mathematical knowledge is poor and so is my understanding of physics described mathematically rather than conceptually. From what I read in that wiki link I thought the quantum potential was being described as a feature of the guiding wave. So I am not sure how it can be done away (it seems to be part of the equation). Perhaps reply to a Demystifier post directly, and he can explain his position concerning it.Are you saying the quantum potential is like the guiding wave where the guiding wave can't affect the quiding wave of different particles? But it seems the quantum potential can affect quantum potential of different particles.. wiki mentioned "David Bohm and Basil Hiley in 1975 presented how the concept of a quantum potential leads to the notion of an "unbroken wholeness of the entire universe", proposing that the fundamental new quality introduced by quantum physics is nonlocality"
So i'm thinking the quantum potential is the cause of your "theoretical explanation of how such "spooky action at a distance" could happen in a physical universe".. but Demystifier seems to say no. So i'm now kinda confused. I'll think about it more. You research it too. Thanks.
according to wiki: https://en.wikipedia.org/wiki/Quantum_potential
"Bohm and Basil Hiley also called the quantum potential an information potential, given that it influences the form of processes and is itself shaped by the environment.[9] Bohm indicated "The ship or aeroplane (with its automatic Pilot) is a self-active system, i.e. it has its own energy. But the form of its activity is determined by the information content concerning its environment that is carried by the radar waves. This is independent of the intensity of the waves. We can similarly regard the quantum potential as containing active information. It is potentially active everywhere, but actually active only where and when there is a particle." (italics in original).[73]"
But Demystifier and other researchers think de Broglie pilot wave approach without quantum potential is more elegant.. but isn't Bohm Quantum Potential also elegant in that this is directly connected to his idea of the Implicate Order? This is closer to AdS/CFT idea than the approach used by Valentini where the quantum vacuum is some kind of fluid of hydrodynamics? Is it not Demystifier? So does it depend on researchers if quantum potential is elegant or not.. or it's just not or never will be elegant?My mathematical knowledge is poor and so is my understanding of physics described mathematically rather than conceptually. From what I read in that wiki link I thought the quantum potential was being described as a feature of the guiding wave. So I am not sure how it can be done away (it seems to be part of the equation). Perhaps reply to a Demystifier post directly, and he can explain his position concerning it.
How come tachyon fields are not theorized to travel faster than the speed of light, while tachyon particles can? May I know what is the explanation based on what you learnt?Regarding tachyon fields I had read in wiki
—
The term "tachyon" was coined by Gerald Feinberg in a 1967 paper[7] that studied quantum fields with imaginary mass. Feinberg believed such fields permitted faster than light propagation, but it was soon realized that Feinberg's model in fact did not allow for superluminal speeds.[6] Instead, the imaginary mass creates an instability in the configuration: any configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as tachyon condensation. A famous example is the condensation of the Higgs boson in the Standard Model of particle physics.
—
But with tachyon particles I assume they are not theorised to undergo tachyon condensation (something only fields do maybe), and their imaginary mass allows faster than light speed in the relativity equations. As I mentioned though, I was just assuming.
I am not sure what it is. Is it supposed to be a field or a particle or something else? My physics is pretty poor, so if you think it might be an answer maybe one of the advisers could help. As I understand it tachyon fields are not theorised to travel faster than the speed of light, only tachyon particles. Apart from spacetime, fields, and particles (in some theories) I am not aware of anything else being said to exist in a physical universe.according to wiki: https://en.wikipedia.org/wiki/Quantum_potential
"Bohm and Basil Hiley also called the quantum potential an information potential, given that it influences the form of processes and is itself shaped by the environment.[9] Bohm indicated "The ship or aeroplane (with its automatic Pilot) is a self-active system, i.e. it has its own energy. But the form of its activity is determined by the information content concerning its environment that is carried by the radar waves. This is independent of the intensity of the waves. We can similarly regard the quantum potential as containing active information. It is potentially active everywhere, but actually active only where and when there is a particle." (italics in original).[73]"
But Demystifier and other researchers think de Broglie pilot wave approach without quantum potential is more elegant.. but isn't Bohm Quantum Potential also elegant in that this is directly connected to his idea of the Implicate Order? This is closer to AdS/CFT idea than the approach used by Valentini where the quantum vacuum is some kind of fluid of hydrodynamics? Is it not Demystifier? So does it depend on researchers if quantum potential is elegant or not.. or it's just not or never will be elegant?
I am not sure what it is. Is it supposed to be a field or a particle or something else? My physics is pretty poor, so if you think it might be an answer maybe one of the advisers could help. As I understand it tachyon fields are not theorised to travel faster than the speed of light, only tachyon particles. Apart from spacetime, fields, and particles (in some theories) I am not aware of anything else being said to exist in a physical universe.How come tachyon fields are not theorized to travel faster than the speed of light, while tachyon particles can? May I know what is the explanation based on what you learnt?
Why didn't you mention about the quantum potential, name123? I heard the quantum potential is non-local in that it can track a particle somewhere in Andromeda galaxy and a particle on earth especially if they are entangled.. so it's like the quantum potential can track all the particles in the universe at once. What do you think?I am not sure what it is. Is it supposed to be a field or a particle or something else? My physics is pretty poor, so if you think it might be an answer maybe one of the advisers could help. As I understand it tachyon fields are not theorised to travel faster than the speed of light, only tachyon particles. Apart from spacetime, fields, and particles (in some theories) I am not aware of anything else being said to exist in a physical universe.
Thanks for your help, and clearing up my misconception (of thinking that the guiding wave/field propagating at faster than light speed was the explanation) :)Why didn't you mention about the quantum potential, name123? I heard the quantum potential is non-local in that it can track a particle somewhere in Andromeda galaxy and a particle on earth especially if they are entangled.. so it's like the quantum potential can track all the particles in the universe at once. What do you think?
Thanks for your help, and clearing up my misconception (of thinking that the guiding wave/field propagating at faster than light speed was the explanation) :)Thank you for asking sharp questions. It's a pleasure to explain things to people who know what confuses them.
Yep.Thanks for your help, and clearing up my misconception (of thinking that the guiding wave/field propagating at faster than light speed was the explanation) :)
So nothing more than an equation that gives the result, no theoretical explanation of how such "spooky action at a distance" could happen in a physical universe?Yep.
There is no mechanism in the mechanical sense. There is only an equation which describes how it happens.So nothing more than an equation that gives the result, no theoretical explanation of how such "spooky action at a distance" could happen in a physical universe?
So what is the suggested mechanism for the first particle altering the second particle's position across that distance?There is no mechanism in the mechanical sense. There is only an equation which describes how it happens.
So the guiding wave for the second particle is no different from how it would have been if the first particle had not been measured?That's correct (except for the technical detail that we cannot really talk about the second-particle wave, because there is only a second-particle density matrix).
Sure, but why should it be in a non-relativistic theory?Where did I say or implied that it should!
No. They are expained by changes of the position of the first particle.So the guiding wave for the second particle is no different from how it would have been if the first particle had not been measured? (sorry if I am being slow here, but just checking that you aren't suggesting that the change in the position of the first particle (rather than its measurement) changes the guiding wave and thereby changes the position of the second particle).
But in BM with the Bell Tests, are the changes to the 2nd particle's position not explained by changes to the guiding wave on measurement of the first particle?No. They are expained by changes of the position of the first particle.
Sure, but why should it be in a non-relativistic theory?
Which speed are you referring to?The speed of propagation of the wave function e.i. the solution of the Schrodinger's equation, in the PDE sense. Compactly supported initial data don't remain compactly supported.
The superluminal influences in Bohmian mechanics are not directly related to tachyons. Tachyons are mentioned only as a well-known counterexample to the frequent claim that superluminal influences contradict relativity.But in BM with the Bell Tests, are the changes to the 2nd particle's position not explained by changes to the guiding wave on measurement of the first particle? The reason I ask is that if they are, and the guiding wave is a field, then the superluminal influence suggested by BM would be ruled out by QFT I think.
The only trouble is that there's no convincing theory of tachyons, and fortunately so far we don't need any to describe nature (at least after the OPERA collaboration has found their bug leading to the claim that neutrinos might be tachyons :biggrin:).
But in BM the guiding wave would (I think) be a field (it is not a particle), and so even if imagined to have an imaginary mass (in order to propagate at faster than light speeds and be compatible with relativity), it would be a tachyon field (not a tachyon particle). And, as I understood it, QFT does rule out tachyon fields propagating at faster than light speeds. Which is why I was checking whether it was being suggested that tachyon particles were involved.The superluminal influences in Bohmian mechanics are not directly related to tachyons. Tachyons are mentioned only as a well-known counterexample to the frequent claim that superluminal influences contradict relativity.
Well, in non-relativistic theory there's no "speed limit", and it's not a contradiction within the non-relativistic theory to have instantaneous interactions (as, e.g., in Newton's model for the gravitational interaction). The only trouble is that it contradicts observations, which clearly prefer relativistic spacetime models over non-relativistic ones.
If they are entangled how are you suggesting that changes to the wave subsystems influence each other at faster than light speeds, because waves are fields are they not, and you have stated that tachyon fields do not propagate at faster than light speed? Are you suggesting that tachyon particles are involved in the entanglement of the wave subsystems?No. The waves do not have superluminal influences on each other. Bohmian particles have.
They are called waves, but the equation is not a wave equation, it isn't hyperbolic to expect finite speed of propagation. In fact, if I am not wrong, it has infinite speed of propagation.Which speed are you referring to? Take a free particle. The dispersion relation is
$$omega=frac{vec{p}^2}{2m},$$
and thus the phase velocity is
$$c_{text{phase}}=frac{omega}{|vec{p}|}=frac{|vec{p}|}{2m},$$
and the group velocity is
$$c_{text{group}}=partial_{|vec{p}|} omega=frac{|vec{p}|}{m},$$
neither of which is infinite.
They are called waves, but the equation is not a wave equation, it isn't hyperbolic to expect finite speed of propagation. In fact, if I am not wrong, it has infinite speed of propagation.Yes, I also understand that, the wave in BM has infinite speed of propagation. But earlier Demystifier had given me a link to a paper in which he had seemed to suggest that QFT did not rule out the type of superluminal influences in BM, and I had asked him about it. He wrote that:
@name123 one should distinguish classical tachyon particle from classical tachyon field. It is true that classical tachyon field does not propagate faster than light. Nevertheless, classical tachyon particle does travel faster than light.But in BM the guiding wave would (I think) be a field (it is not a particle), and so even if imagined to have an imaginary mass (in order to propagate at faster than light speeds and be compatible with relativity), it would be a tachyon field (not a tachyon particle). And, as I understood it, QFT does rule out tachyon fields propagating at faster than light speeds. Which is why I was checking whether it was being suggested that tachyon particles were involved.
If they are entangled how are you suggesting that changes to the wave subsystems influence each other at faster than light speeds, because waves are fields are they not, and you have stated that tachyon fields do not propagate at faster than light speed? Are you suggesting that tachyon particles are involved in the entanglement of the wave subsystems?They are called waves, but the equation is not a wave equation, it isn't hyperbolic to expect finite speed of propagation. In fact, if I am not wrong, it has infinite speed of propagation.
There is only one wave for the whole system, but when the system consists of non-entangled subsystems the wave can be decomposed into separate waves for each subsystem.If they are entangled how are you suggesting that changes to the wave subsystems influence each other at faster than light speeds, because waves are fields are they not, and you have stated that tachyon fields do not propagate at faster than light speed? Are you suggesting that tachyon particles are involved in the entanglement of the wave subsystems?
There are multiple guiding waves? I had thought there was one for the universe, and that it appeared random because there was no way to have all the information about all the non-local influences. Are you suggesting each particle has its own guiding wave, and that particle guiding waves can become entangled? If so how do they become entangled and disentangled?There is only one wave for the whole system, but when the system consists of non-entangled subsystems the wave can be decomposed into separate waves for each subsystem.
On page 7 under the Non-locality section it states:
"Since the wavefunction is defined on the configuration space, the guidance equation of an N-particle system links the motion of every particle to the position of the other particles at the same time". Is this only if the N-particles are entangled?Yes.
In the same section it goes onto state:
"Finally does the non-locality of the de Broglie-Bohm theory vanishes if the state is not entangled."
Which seems like a question, but perhaps the "does" can be removed and it would be a statement. Is this how you would read it?Yes.
It is ensured by the fact that wave functions (i.e. guiding waves) associated with different measurements are not entangled with each other.There are multiple guiding waves? I had thought there was one for the universe, and that it appeared random because there was no way to have all the information about all the non-local influences. Are you suggesting each particle has its own guiding wave, and that particle guiding waves can become entangled? If so how do they become entangled and disentangled?
Before asking further questions, read also this:
https://arxiv.org/abs/quant-ph/0611032On page 7 under the Non-locality section it states:
"Since the wavefunction is defined on the configuration space, the guidance equation of an N-particle system links the motion of every particle to the position of the other particles at the same time". Is this only if the N-particles are entangled?
In the same section it goes onto state:
"Finally does the non-locality of the de Broglie-Bohm theory vanishes if the state is not entangled."
Which seems like a question, but perhaps the "does" can be removed and it would be a statement. Is this how you would read it?
It seemed from what I read that it is suggested that the measurement of the first particle would instantaneously change the measured position of the second particle.Yes.
I was imagining a non-local guiding wave influencing a population of particles, and the measurement influencing the non-local guiding wave.Velocity of each particle is determined by position of that and other particles. But the rule of this determination is not fixed. It is defined by the guiding wave. The guiding wave guides both the measured particles and the particles constituting the measuring apparatus.
1) If a thousand Bell Tests were done simultaneously (the first particles measured) what ensures that the measurement of second particles will not be influenced by changes to the pilot wave by the other tests (or whatever else is going on in the universe)?It is ensured by the fact that wave functions (i.e. guiding waves) associated with different measurements are not entangled with each other.
2) How is it explained that the change to the pilot wave will influence the position of the entangled second particle such that it will be measured as having the opposite spin to the entangled first particle no matter whether without the altered guidance the second particle would have have "spun up or down"?It is ensured by the entanglement of the wave function, which is explained by the Schrodinger equation … but if this looks too abstract for you, well, some aspects cannot be properly understood without the math.
Yes.
For more details about spin in BM see
https://arxiv.org/abs/1305.1280
Even if you skip equations, you have a lot of text to read and pictures to see.Thanks for the link.
It seemed from what I read that it is suggested that the measurement of the first particle would instantaneously change the measured position of the second particle. What I am not clear on is the suggested mechanism for the measurement of the position of the first particle influencing the measurement of the position of the second particle. Perhaps I am simply misunderstanding the basics. I was imagining a non-local guiding wave influencing a population of particles, and the measurement influencing the non-local guiding wave.
If I have not misunderstood the basics, then a couple of points I am not clear on are:
1) If a thousand Bell Tests were done simultaneously (the first particles measured) what ensures that the measurement of second particles will not be influenced by changes to the pilot wave by the other tests (or whatever else is going on in the universe)?
2) How is it explained that the change to the pilot wave will influence the position of the entangled second particle such that it will be measured as having the opposite spin to the entangled first particle no matter whether without the altered guidance the second particle would have have "spun up or down"? I presumed the alteration required to get the effect would depend upon what position the second particle had prior to the alteration being made.
The problem with tachyons in local QFT is that for the interacting case, as far as I know, one cannot define the S-matrix in the usual way, because it's hard to define Hamiltonian densities that commute at spacelike separated arguments, which is (at least) a sufficient condition for having a Poincare invariant unitary S-matrix fulfilling the linked-cluster principle. See, e.g.,
https://academic.oup.com/ptp/article-pdf/45/5/1646/5399190/45-5-1646.pdf
When you talk about the standard interpretation of QFT did you mean that all particles are fields?Yes.
So regarding the position, in BM do the entangled particles have some associated value which will determine whether they will have their position measured as an up or down spin prior to measurement (perhaps some trajectory), such that if they were measured along the same orientation their measured positions could be interpreted as different spins? Or is it that there is some suggested mechanism for changing the measured position to give an up or down spin interpretation dependent on the measurement of the other? If the latter how is it suggested that the particle that is to have its "spin state"/position changed singled out so that it is its position that is changed and not some other particle's?For more details about spin in BM see
https://arxiv.org/abs/1305.1280
Even if you skip equations, you have a lot of text to read and pictures to see.
@name123 one should distinguish classical tachyon particle from classical tachyon field. It is true that classical tachyon field does not propagate faster than light. Nevertheless, classical tachyon particle does travel faster than light.In the paper you wrote:
"Of course, QFT alone with its standard purely probabilistic interpretation certainly does not describe such superluminal influences, but it does not exclude their existence either (unless, of course, you assume that QFT with its standard interpretation is the ultimate theory of everything)."
When you talk about the standard interpretation of QFT did you mean that all particles are fields?
Concerning the spin measurement in BM, the spin actually never exists in a fundamental sense. That's related to the fact that spin is measured by the Stern-Gerlach apparatus which really measures the position of the particle, while the association of spin with a measured position is just a convenient interpretation.So regarding the position, in BM do the entangled particles have some associated value which will determine whether they will have their position measured as an up or down spin prior to measurement (perhaps some trajectory), such that if they were measured along the same orientation their measured positions could be interpreted as different spins? Or is it that there is some suggested mechanism for changing the measured position to give an up or down spin interpretation dependent on the measurement of the other? If the latter how is it suggested that the particle that is to have its "spin state"/position changed singled out so that it is its position that is changed and not some other particle's?
The point of the SG apparatus is to entangle the particle's spin-##z## component (homogeneous part of the magnetic field in ##z## direction) with the particle's position, and thus you can filter out particles with well-determined spin-##z## values. The association between spin and position is very much straight forward without any reference to pilote-wave or de Broglie Bohm. It's completely understandable and analytically (semi-numerically) calculable from the time-dependent Schrödinger equation alone!
@name123 one should distinguish classical tachyon particle from classical tachyon field. It is true that classical tachyon field does not propagate faster than light. Nevertheless, classical tachyon particle does travel faster than light.
Concerning the spin measurement in BM, the spin actually never exists in a fundamental sense. That's related to the fact that spin is measured by the Stern-Gerlach apparatus which really measures the position of the particle, while the association of spin with a measured position is just a convenient interpretation.
Even with a poor knowledge of physics you may try reading my
https://arxiv.org/abs/1002.3226
because it contains a dialogue with no equations.Thank you for the link to the article which I found useful. Though I still have some problems in understanding the idea you were suggesting (the answers might have been in the equations (which I do not understand)).
You wrote:
—
O: The theory of relativity implies that nothing can travel faster than light.
R: No, the theory of relativity does not imply that. The best known counterexample is
a tachyon, hypothetical particle with mass squared m[SUP]2[/SUP] < 0. It is a completely relativistic
object, and yet it travels only faster than light.
—
But when checking up on them in wiki (https://en.wikipedia.org/wiki/Tachyonic_field) I read:
—
The term "tachyon" was coined by Gerald Feinberg in a 1967 paper[7] that studied quantum fields with imaginary mass. Feinberg believed such fields permitted faster than light propagation, but it was soon realized that Feinberg's model in fact did not allow for superluminal speeds.[6] Instead, the imaginary mass creates an instability in the configuration: any configuration in which one or more field excitations are tachyonic will spontaneously decay, and the resulting configuration contains no physical tachyons. This process is known as tachyon condensation. A famous example is the condensation of the Higgs boson in the Standard Model of particle physics.
—
Is this simply a case of different theories different suggestions?
Also I think that non-local effects occur in both QFT and Bohmian Mechanics, but I am not sure of the Bohmian mechanics interpretation of the Alain Aspect experiment (where I think spin states were measured), given Bell's inequality theorem. In Bohmian Mechanics, do the entangled particles not have a spin state prior to measurement, or is it that there is some suggested mechanism for changing the spin state of one dependent on the measurement of the other? If the latter, how is it suggested that the particle that is to have its spin state change singled out so that it is its state that is changed and not some other particle's?
I can understand why Einstein assumed that a physical universe in which nothing could travel faster than the speed of light would not have the "spooky action at a distance" suggested by Bohmian mechanics. Do you think "spooky action at a distance" is compatible with a physical universe in which nothing could travel faster than light? If so would you mind explaining how you think it would work?
(P.S. my knowledge of physics is pretty poor)Even with a poor knowledge of physics you may try reading my
https://arxiv.org/abs/1002.3226
because it contains a dialogue with no equations.
Demystifier submitted a new PF Insights post
How I Stopped Worrying and Learned to Love Orthodox Quantum Mechanics
View attachment 210012
Continue reading the Original PF Insights Post.I can understand why Einstein assumed that a physical universe in which nothing could travel faster than the speed of light would not have the "spooky action at a distance" suggested by Bohmian mechanics. Do you think "spooky action at a distance" is compatible with a physical universe in which nothing could travel faster than light? If so would you mind explaining how you think it would work?
(P.S. my knowledge of physics is pretty poor)
You are basically asking why the detector in the double slit experiment can only detect one electron and not have multiple hits for only one electron emitted. But isn't it that according to:
1. Bohmian Mechanics.. there is a trajectory for the one electron being emitted so it hits the detector at one point…
2. Many Worlds.. there are multiple hits in the screen.. but we only viewed one of them because we are entangled with only one of them…
3. Copenhagen.. the wave function may pass through both slits but it collapses into one hit when it reached the screen…Yes, I'm mostly saying why I find the "minimal interpretation" inadequate. Those three have different issues.
(please always mention de Broglie too, he's the originator of the pilot-wave idea!)Don't you know about the Stigler’s law?
https://en.wikipedia.org/wiki/Stigler's_law_of_eponymy
It is not clear that QED with Poincare invariance exists as a theory in itself – even without data, we seem to need a cutoff to make sense of it. If we take say lattice QED with the lattice spacing near the Landau pole scale, the theory is FAPP Poincare invariant at low energies. But because of the lattice, it is not even true that the theory is Poincare invariant below the cut off – already near the Landau pole there should be huge violations of Poincare invariance. So it is only far, far, far below the cutoff that QED is Poincare invariant.I would like to reformulate the issue in the following way. Classical electrodynamics is Poincare invariant. If the corresponding quantum theory is not Poincare invariant, it should manifest as a quantum anomaly. Quantum anomalies are a well developed subject in QFT, but I never heard of an anomaly related to Poincare invariance. Yes, you need to introduce a cut-off that seems to spoil the invariance, but if there is no anomaly then it looks like a formal nitpicking without direct physical consequences.
Yes, it is the Wilsonian view that says QED need not come from a Poincare invariant theory, ie. the Poincare invariance may exist as an approximation at very low energies.That's what I'm saying all the time!
In other words, one cannot use the low-energy Poincare invariance of QED as an argument against Bohmian Mechanics.Well, I don't think that de-Broglie-Bohm mechanics (please always mention de Broglie too, he's the originator of the pilot-wave idea!) has any merits beyond (non-relativistic) QM in the minimal interpretation, and it's hard to find a convincing interpretation in the context or relativistic QFT. Why should I adopt an interpretation which is less comprehensive than standard (relativistic) QFT without any additional merit for the description of nature?
I'd not say that Newtonian physics is false. It has only a known range of applicability.
I don't understand your statement about QED. It's manifestly Poincare invariant. We know, it breaks down at a large energy scale, where it has a Landau pole, and that's for sure some range of applicability of renormalized perturbative QFT. Whether it exists beyond the perturbative approach is unknown (and perhaps even not very probable). We don't know it's precise range of validity yet, because we don't have observations where it (or better said the Standard Model as a whole) really fails and in which way.